Low Power

You are building advanced chips for machines. Making the
chips is easy, but the power supply turns out to be an issue
since the available batteries have varied power outputs.

Consider the problem of $n$ machines, each with two chips,
where each chip is powered by $k$ batteries. Surprisingly, it does
not matter how much power each chip gets, but a machine works
best when its two chips have power outputs as close as
possible. The power output of a chip is simply the smallest
power output of its $k$
batteries.

You have a stockpile of $2nk$ batteries that you want to
assign to the chips. It might not be possible to allocate the
batteries so that in every machine both chips have equal power
outputs, but you want to allocate them so that the differences
are as small as possible. To be precise, you want to tell your
customers that in all machines the difference of power outputs
of the two chips is at most $d$, and you want to make $d$ as small as possible. To do this
you must determine an optimal allocation of the batteries to
the machines.

Consider Sample Input 1. There are $2$ machines, each requiring
$3$ batteries per chip,
and a supply of batteries with power outputs $1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11,
12$. You can, for instance, assign the batteries with
power outputs $1, 3, 5$ to
one chip, those with power $2, 4,
12$ to the other chip of the same machine, those with
power $6, 8, 9$ to the
third chip, and those with power $7, 10, 11$ to the fourth. The power
outputs of the chips are $1, 2,
6$, and $7$,
respectively, and the difference between power outputs is
$1$ in both machines. Note
that there are many other ways to achieve this result.

Input

The input consists of a single test case. A test case
consists of two lines. The first line contains two positive
integers: the number of machines $n$ and the number of batteries per
chip $k$ ($2nk \leq 10^6$). The second line
contains $2nk$ integers
$p_ i$ specifying the
power outputs of the batteries ($1 \leq p_ i \leq 10^9$).

Output

Display the smallest number $d$ such that you can allocate the
batteries so that the difference of power outputs of the two
chips in each machine is at most $d$.